Digital signal processing is undertaken or used in many every day life devices, as well as in many special purpose devices, such as medical imaging devices.
In signal processing, both a signal to be measured and the measurement process itself may contain and/or contribute noise. It is advantageous to eliminate noise to obtain better signal processing results, such as sharper images. In some applications the process of signal measurement requires a significant amount of time, such as in medical equipment known as MRI. Therefore, it would be also advantageous to decrease the number of required signal measurements for a given quality of result, as well as achieve the same sharpness and number of pixels with fewer signal measurements.
If a measured signal is to be transferred to some other location, it is also advantageous if the data to be actually sent is as small as possible to lower the required bandwidth, or to increase the rate of sending of complete measurements, such as the frame rate for video signal transmissions.
Sparse representation of signals is a signal processing art in which noise, which can not be represented sparsely, can be filtered out. The sparse representation of a given signal can be estimated from a small number of measurements, where small is compared to the dimension of the signal. Also, a sparse representation generally means that the data is compressed.
There are numerous sparse representation learning algorithms known in the art. These algorithms, however, are not scalable to million dimensional inputs. Also, these algorithms have not been shown to learn the sparse representation that generated the input on artificial data sets; that is, the correctness and convergence of learning is neither demonstrated nor mathematically proven.
There are known hardware designs for operating on large data sets, e.g. large matrix multiplications and neural network simulations. Neural network simulators are known that typically use mixed analog-digital signals, but these make it harder to scale up the hardware. Also, in digital signal operations the bandwidth with which data can be downloaded to the hardware limits the practical size of the hardware.
It is an object of the present invention to provide a method which results in a sparse representation for a measured signal that scales for million dimensional inputs.
It is a further object of the present invention to provide an apparatus that can realize this method.